# Stored data for newform 4001.2.a.b, downloaded from the LMFDB on 24 April 2024.
{"label": "4001.2.a.b", "space_label": "4001.2.a", "level": 4001, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660928929, "dim": 184, "analytic_rank": 0, "is_twist_minimal": true, "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16004, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 31.948145848714283, "level_radical": 4001, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [4001, 1, [3], [1]], "inner_twist_count": 1, "level_primes": [4001], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 184, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[4001, -1]], "trace_display": [3, 28, 15, 49], "traces": [184, 3, 28, 217, 15, 31, 49, 6, 210, 46, 25, 61, 52, 28, 59, 279, 16, -2, 86, 26, 22, 54, 55, 72, 241, 32, 97, 75, 27, -10, 276, 0, 20, 122, 30, 278, 42, 14, 113, 115, 39, 15, 65, 32, 54, 65, 82, 117, 297, 4, 45, 136, 21, 93, 252, 74, 14, 54, 95, 58, 131, 14, 88, 368, -9, 52, 90, 27, 101, 18, 117, -15, 72, 7, 150, 148, 7, 22, 287, 43, 244, 86, 25, 14, 41, 25, 82, 115, 48, 78, 272, 69, 44, 161, 37, 129, 106, -46, 53, 325, 29, -26, 354, 44, 9, 41, 13, 133, 137, -19, 184, 65, 3, -5, 123, -13, 107, 44, 102, -91, 295, -6, 17, 521, 9, 45, 169, -60, 101, 20, 70, -8, 101, -33, 217, 313, -12, -74, 340, -46, 57, 22, 59, 338, 59, 89, 109, 50, -21, 22, 339, -13, -26, 64, 47, 92, 87, -97, 262, 189, -24, -103, 92, 19, 2, 110, 186, -68, 312, -3, 153, 16, 46, 54, 204, -57, 6, 42, 140, -13, 314, -119, 110, 132, 50, 4, 139, 72, -14, 50, 108, 103, 95, -41, 28, 451, -37, -30, 718, -100, 49, 108, 11, 5, 38, -24, 213, 205, 47, -71, 231, -73, -12, 78, 111, 169, 61, -91, 75, 351, 9, -131, 323, 78, 198, -35, 37, -141, 202, -115, 355, 73, -92, -8, 161, 63, -23, -2, 102, -135, 209, -171, 204, 273, -56, -48, 145, -97, -39, 40, 127, -198, -1, -44, 138, 429, 35, -185, 300, -208, -6, 37, 32, -62, 215, -192, -10, 50, 105, -353, 406, -103, -115, 184, 2, 50, -1, -88, 760, -118, -69, -155, 191, -5, -87, -11, 112, -197, 340, -155, 40, -18, -53, -112, 398, -112, -2, -53, 110, 84, 221, -180, 145, 217, -117, 56, 142, -95, -7, -119, 382, -157, 185, -94, -33, 345, -39, -129, 260, -174, 28, -7, -11, 241, 154, -106, 153, 128, -90, -288, 221, -105, -64, 275, 355, -268, 129, -174, 289, -22, 10, -126, 218, -28, -62, 63, -7, -179, 212, -230, 312, 113, -9, -102, 328, 49, -107, -124, 85, -42, 326, -114, 118, 435, -190, -96, 487, -140, 5, -100, 80, -184, 1, -92, 179, 316, 18, -242, 277, -183, 57, -116, 95, 91, 34, -83, 52, 89, -25, -287, 630, -322, -90, 239, -14, -167, 131, -117, 374, 241, -34, -164, 123, -185, -49, -8, 53, -180, 213, -350, 165, 500, -152, -149, 376, 37, -119, -135, 126, -342, 138, -150, 296, -10, -136, -113, 128, -214, -118, 166, 100, 43, 141, -79, -112, 194, -89, -281, 924, -422, 247, -198, -92, -23, 167, -20, 104, -34, 5, -499, 377, -271, -188, 344, 74, -323, -62, -248, -104, -17, 37, -477, 338, -240, -25, 167, -18, -2, 245, -212, 290, 62, -257, -156, 200, -222, -100, 15, 96, -523, 128, -201, -194, 315, -94, -39, 392, -73, 67, -83, -67, -244, -20, -361, 360, 813, -194, -308, 283, -291, -242, -63, 130, -233, -65, -236, 142, 51, 25, -471, 731, -390, -291, -26, -100, 14, 15, -375, 82, -152, -27, -276, 158, -45, -258, 4, -14, -413, 283, -282, 283, 1, -132, -432, 397, -326, -13, -8, -80, -134, 8, 47, -70, 555, -177, -401, 147, -153, 29, 16, 253, -518, -9, -214, -61, 555, -178, -345, 731, -352, -146, -171, -35, -181, 90, -179, 78, -148, -105, -485, 237, -359, -55, -75, 145, -60, -10, -358, -1, -327, -70, -425, 231, 29, -423, 249, -49, -245, 124, -461, 299, -238, -189, -358, 172, -313, -133, -118, 160, -384, 368, -315, -119, 334, -221, -590, 555, -407, -159, -159, -42, -548, -44, -259, 257, 34, -206, -400, 292, -387, 68, -142, 61, -282, 278, -269, -177, -64, -132, -689, 486, -533, -236, -43, -109, -11, 54, -432, 309, 18, -182, -415, 249, -598, -372, 30, 96, -566, 298, -331, -177, -41, -184, -349, 114, -212, -104, -326, -52, -653, 235, -401, 77, 68, -227, -503, 124, 26, -196, -144, 143, -606, 72, -219, 279, 275, -76, -562, 474, -480, -316, -69, -113, -328, 72, -3, 26, -340, -262, -768, 651, -153, -250, -148, -205, -169, -142, -428, 145, -321, -254, -476, 651, -468, -14, -77, -144, -557, 216, -610, 434, -173, -209, -733, -162, -100, -330, -257, 556, -537, 143, -453, -259, 651, -238, -400, 326, -729, -63, -324, 43, -568, -80, -376, -133, -182, -252, -311, 47, -156, -40, -239, 69, -434, 192, -431, -174, -114, -97, -747, 844, -319, -283, 136, -76, -757, -17, -480, 403, -190, -161, -505, 42, -292, -436, 16, -113, -304, 202, -676, 143, 13, -169, -484, 1018, -414, -356, -450, -145, -839, 53, -434, -111, 400, -288, -554, 124, -592, -107, 112, -25, -851, -93, -339, -197, 960, -68, -905, 275, -747, -249, -326, -249, -594, -200, -550, -80, -138, -224, -575, 207, -506, -334, -461, 71, -573, -47, -412, 323, -449, -130, -757, 382, -439, -394, -244, -94, -261, 443, -563, 285, 103, -426, -649, -40, -345, -74, -262, 274, -953, 183, -637, -297, 118, -202, -434, 239, -671, -227, -148, -97, -512, -83, -486, -228, 46, -189, -997, 643, -413, -323, -444, -84, -263, -167, -310, -163, -520, -211, -914, 757, -605, -70, 147, -376, -602, -92, -541, -282, 173, -34, -1003, 125, -487, -267, -216, 179, -735, 27, -710, -308, 6, -386, -516, 726, -267, -576, -176, -100, -610, 137, -518, -216, -417, -306, -215, 77, -569, -173, -652, 183, -1002, -32, -435, -366, 246, -265, -1092, 454, -657, -349, -220, -107, -97, -209, -368, 540, -396, -67, -1007, 245, -759, -202, -238, -332, -623, -246, -586, -280, -171, -190, -922, 299, -349, -507, -230, -321, -714, 147, -515, 270, -511, -407, -553, 123, -475, -405, -132, 105, -1056, 422, -574, -394, 204, -243, -778, -69, -932, -224, -704, -36, -414, -214, -503, -225, 195, -226, -700, 655, -968, -199, -366, -113, -776, -120, -514, -471, -545, -335, -1096, 1249, -539, -387, -473, -254, -855, -12, -711, 212, -269, -409, -582, -241, -223, -250, 66, -133, -1155, -13, -505, 142, -559, -121, -299, 684, -337, -438, -228, -158, -349, 264, -537, -138, 282, -464, -318, 155, -194, -161, -434, -151, -961, -234, -119, -238, 249, -317, -403, 1353, -600, -180, -206, -145, -374, -353, -135, -156, -199, 54, -272, 279, -320, 9, 62, -82, -581, -10, -225, 59, 249, -32, -389, 524, -362, -397, -251, -10, -334, 115, 141, 31, -263, -338, -80, -10, 203, -238, 3, 189, -854, 265, -324, 16, 479, -160, -397, 174, -305, 43, -277, 183, -514, 130, -11, 142, 445, -132, 81, 129, -188, -164, -190, -88, 85, -177, -70, -289, -376, 15, 1, 921, -288, -412, 131, -312, 1247, -87, -81, 293, -590, -351, -427, 108, 218, -141, -29, 222, -161, 81, -218, -298, 239, 106, 86, 412, -308, -152, 152, 190, -104, 68, -343, 161, -38, -216, 12, 191, 110, -152, -109, 236, -578, 278, 263, -622, 543, -461, -171, 939, -227, 112, 145, -95, -289, -201, -159, 535, 137, 119, -550, 532, -396, 123, 192, 182, -59, -203, 157, -193, 758, 42, 163, 389, -232, -542, 513, -257, 328, 206, 8, 185, -232, 31, 562, 115, 118, -73, -66, 243, -154, 89, 68, -178, 319, 145, -115, 326, -142, 5, 297, -115, -236, 2, -81, 375, 289, -336, 60, 582, -738, 14, 53, 4, 901, 176, -79, -322, 148, -160, 57, 1434, 149, -171, -169, -192, 11, -15, 178, 88, -233, -365, -864, -58, 842, 133, 86, -89, 747, 287, -113, 487, 484, 53, 360, 312, -201, -343, -258, 199, 250, -42, -260, 383, 515, -302, 344, 197, 37, 93, 436, 291, -541, 118, 170, -372, -51, -176, 519, 590, -175, -351, -37, -170, 137, -10, 218, -140, -79, -287, 104, 810, 34, 69, 574, -105, 371, -169, -290, 257, 669, 21, -427, 497, 273, -286, 142, -168, 965, -34, -351, -267, 183, 148, 430, 196, 14, -153, -4, 329, -800, 305, -73, 402, 441, -100, -277, 291, -355, 258, -134, 117, -314, -64, -10, -10, 905, -375, 641, 53, 917, -413, 27, 305, 391, -110, -63, 239, 830, -10, 423, 895, -726, -291, 437, -245, 643, 96, 437, 815, 0, -130, -384, 136, 545, -144, 175, 228, -105, 604, 470, 219, -35, 9, -73, 1027, 321, -457, 680, -281, 349, -47, 16, 95, 176, -275, 202, 369, 35, 1, 368, 686, 326, 148, 100, -429, 159, -144, 293, 1293, -42, -66, -89, 133, 661, -289, 421, -87, 273, -226, 122, 404, -33, 246, 550, 77, 35, 75, 366, -8, 756, -49, -254, 394, 36, -342, 295, -102, 313, 199, -471, 576, -370, 29, 750, 326, 204, -513, 102, 539, -217, 172, 27, -326, 535, -145, 83, 194, 1384, -477, -83, -234, 311, -11, 218, 920, 787, -28, 464, 764, -378, 87, -167, 69, 451, -164, 435, -17, 905, -46, 52, 581, -468, 17, 185, 398, 221, -152, 545, 546, -367, -367, -627, 415, 350, -199, 104, -95, 785, 217, 787, 109, -39, -21, 663, 279, -291, -276, 119, 100, 114, 357, 245, 937, 741, -674, -402, -78, 276, 216, 249, 667, -452, -7, 272, -322, 471, -318, 1168, 1446, 649, -187, -294, -243, 338, 328, 32, 90, -109, -17, 355, 426, -108, 201, 179, -94, 383, -198, 114, 132, 358, -340, -765, 937, 343, -520, 527, 109, 454, 138, -168, 159, 217, -44, 261, -112, -112, -233, -70, 542, -54, 187, -323, 11, 1095, -129, 108, 1120, 410, 151, 135, 313, -416, 141, 972, -112, 755, -335, 437, 256, -291, -298, -292, 274, -796, 83, -30, -10, 742, -30, 398, 768, -473, 51, -81, 85, 1097, -342, 375, 479, 337, -132, 611, -75, 223, -424, 210, 148, 977, 649, 332, 609, -266, -124, 454, 769, -528, -639, 6, -166, 693, 204, 105, 677, 61, -337, 3, 302, 1576, 331, 115, 308, -471, -53, 97, 66, 405, 125, -10, 648, -741, -378, 58, -8, 1914, -343, 433, 169, 780, -145, 249, 734, -349, -73, 254, 664, 745, -83, 369, 543, 39, -483, -390, 456, 899, 276, 535, -142, 191, 176, 690, 387, 36, -60, 1285, 157, 525, -403, 329, 371, 57, 387, 183, 89, 484, -316, 1160, 423, 614, -274, 11, 48, 25, 296, 70, 43, -28, -146, 1026, 896, 1232, -329, -462, 176, -83, 116, -27, -103, 998, -129, -163, 1243, -366, -194, 1017, -250, 173, -343, 540, 496, 1175, -168, 879, 21, 187, -82, -197, -43, 676, 8, 315, -45, 158, -256, 528, 612, 215, -35, -88, 340, 291, 519, -128, 429, 583, -316, -155, 1, 141, -86, 158, 245, -427, -58, 1471, 20, 1817, -571, 1129, 585, -139, -224, -122, 594, 849, 176, 53, 256, -127, 0, 186, -39, -2, -355, 726, 103, 278, 37, 812, -223, 275, -271, -552, 661, 797, -938, -60, -509, 436, 69, 443, 1540, -176, -443, 589, -63, 412, -173, 967, 563, 640, -289, -545, -111, 780, -374, 912, 768, -416, -100, 138, -252, -492, -49, -301, 52, 915, 28, 735, 1275, 99, -124, -97, 121, 595, 118, 1220, -211, -189, -283, -393, 926, -261, -323, 539, -182, -197, -342, 761, 330, 978, -201, -14, 396, 1163, -568, 107, 14, -440, 415, -506, 233, 730, -119, 900, 731, -344, -698, 552, 68, 20, -166, 112, 206, 741, -506, 782, 108, 727, 306, 335, 421, -362, 315, 383, 257, 632, -372, 264, 1247, 945, -298, 280, -272, 1619, -683, 160, -214, 369, 106, -71, 354, -935, 18, 608, 43, 320, -171, 1456, 161, -413, -253, -477, 840, -227, -656, 43, 75, 1571, 458, 1115, 326, -81, -198, 149, 433, 515, -440, 48, 395, 184, 326, -528, -256, 395, -422, 210, 179, -35, 16, 555, -59, -444, 114, 854, 309, 661, -635, 1857, 359, -117, -389, -132, 244, 843, -6, 161, -454, 464, -96, 1757, 1592, 800, -293, 107, -417, 247, -401, 498, 1306, 297, -194, 20, 256, 182, -70, 523, 149, 1202, -72, -22, 104, -34, 185, 282, 855, -833, -723, -240, 496, 1165, -170, 66, 25, 1388, -246, 13, 9, 1763, -221, -131, 132, -137, -117, 1289, -546, 626, -353, 252, 762, -752, -587, -451, 82, -42, 142, 499, 348, 878, -292, 302, 404, 165, -98, 639, 243, -287, -252, -174, -316, 178, -380, -2, -8, 399, -549, 559, -78, 1189, 725, 997, 390, -565, -307, 289, 151, 539, -520, 156, 102, -576, -82, 261, 381, 1556, -382, -136, 609, -139, -290, 709, 177, -818, -76, -29, 259, -193, -607, 125, 165, 666, -250, 342, 41, 1549, -448, 357, -649, -110, 125, 4, 1689, -704, 180, -67, -209, -190, 93, 392, 1075, -702, -566, -172, 53, 271, -277, 363, -166, 594, 425, 1262, -528, 355, -124, 971, 219, 840, -951, -69, 75, -113, 178, -529, 222, 630, -263, 881, -210, 729, -506, -512, 191, -1054, -131, 1325, 388, 272, -524, 2093, 1487, -517, -319, -457, 149, 911, -373, -120, -119, 638, -199, 106, 747, -10, -384, 74, -479, -43, -282, 454, 319, 577, 296, -285, 423, -320, -509, -214, -288, 1716, -46, 1326, 120, -497, -285, 111, 148, -807, -379, -222, 833, 526, 569, -191, -392, -5, -626, 527, -68, 545, 188, 217, -263, -57, -299, 201, -112, 1705, -346, 231, 71, 164, 260, -119, 949, -331, -337, -127, 10, 11, -177, 290, 960, 606, -523, 135, 225, 394, -154, 787, -115, -406, -293, 121, 678, 1370, -485, 164, -90, -271, 150, -242, -364, -444, -283, 675, 705, 555, -475, 472, -309, 1113, -429, -555, -97, 1065, -119, -34, -214, 12, -185, -373, 418, -179, -50, 460, -153, 1128, -332, 304, 1663, 1208, -894, -323, -385, 1482, -444, -105, 3, -78, -49, 177, 251, -669, -175, -107, -11, -623, -400, 1798, 292, 441, -491, 905, 149, -155, -522, 561, 164, 1178, 213, -449, 1131, 44, -119, 2190, 486, -167, -587, 54, -231, 236, 257, -350, -142, 95, -198, 170, 326, 682, -277, -551, -135, -355, -131, 1317, 214, -677, -322, 1014, 216, 1605, -577, 28, 440, -140, -161, -134, -399, -146, -126, 1148, 1093, -370, -195, 152, -265, 1067, -481, 454, 123, -1044, -374, -662, 160, 286, -489, 763, -382, 1373, -277, 1236, -172, 98, -281, 317, 274, 185, -99, -33, 271, -1070, 83, -569, 293, 977, -576, 828, -145, 797, -90, 580, 270, 614, -257, -230, -448, 149, -373, 1479, 1169, -357, -545, -459, 187, 200, -248, 808, -271, -320, 157, 532, 728, -99, -457, -13, -316, -619, -386, 570, 402, 48, -447, -598, 1158, 827, -33, -362, -494, 526, -186, -35, 315, -323, 191, 353, -28, -422, -1026, 587, -43, 571, 268, 1079, -252, 1766, -367, -259, 757, -334, -581, -169, -245, -637, 88, 930, -93, 150, -647, 184, 383, 198, 609, -382, 64, -891, -82, 287, 197, 1177, -400, -25, 1013, -1452, -298, 503, -129, 936, -539, 749, 732, 244, -501, 153, 164, 1008, -849, -595, 257, -152, 634, -438, -516, -544, -399, -381, 399, 915, -802, -169, -184, -302, -107, -452, 362, 68, -630, 410, 28, 152, 346, 153, 218, -1068, -103, 502, -642, 128, -290, 1974, 1472, -67, -831, 162, -277, 662, -804, -105, -104, -107, 30, 356, 557, 598, -564, -496, 127, 126, -631, 665, -607, 480, -268, 170, 441, 118, -620, -12, -386, 1219, 109, 940, 1220, -551, -468, 1387, -587, -490, -368, -175, 1209, -534, -94, -367, 132, 603, -716, 1619, 195, 416, -849, -364, -390, -233, -41, 446, 177, 79, -221, 1048, 1072, 685, -921, -678, -159, 108, -67, 14, -23, 412, -593, -158, 821, -881, -565, 1144, 466, 319, -294, 483, 154, -382, -208, -727, -458, -567, -1121, 610, -252, 674, -134, -166, -107, 151, 146, 57, 1731, -1354, -317, -375, 118, 1263, -286, 1524, 253, -54, -672, 48, 104, 485, 50, -526, 129, -1201, -751, 687, -253, 773, -623, 218, 859, 289, 171, -548, -110, -512, -384, -549, -642, 11, -477, 853, 722, -535, -211, -349, -530, -508, 49, 2008, 271, -281, -268, 46, 1396, -80, -386, -613, -382, -479, -135, -612, 502, 42, -1, 503, 485, 663, -1115, 842, -66, 77, -121, -394, -270, 108, -110, -178, 243, 76, -119, -77, -76, 172, -306, 1101, 334, -394, -457, 537, 876, -611, -663, 132, 313, 605, -496, -154, -731, 830, -391, -261, 701, 282, 254, 177, -559, -338, -149, 1108, 811, 642, -540, -715, -405, -372, -460, 276, 242, 156, 132, 1903, 265, 54, -231, 714, 1085, -880, -849, 4, 3, 367, 263, -486, 445, 59, -811, 320, -186, 2098, 449, 32, -221, -1123, -163, -271, 230, 319, -553, -274, 1544, -3, -553, 231, 102, 592, -446, -15, 294, -130, 119, 308, 377, -923, 16, 597, 444, 248, -1049, 290, -348, 427, -854, 1113, 949, 2923, -1118, -188, -854, 1894, 52, 401, 540, -1282, -478, -751, -217, -360, -266, -10, 220, -2395, 176, 87, -347, 1576, -507, 1103, 25, 611, -438, 138, 132, -1217, -302, -344, -113, -837, -718, 2229, 176, 141, -374, -678, -196, 218, -153, 536, 12, -442, -128, 1599, 1493, -560, -761, 350, -522, -228, -748, 447, 1462, -1393, -278, -1060, 205, -399, -551, 68, -481, 477, 503, 28, -137, 793, -541, -355, 83, -378, -650, 1594, 198, 2118, -5, -58, -204, 9, -420, -308, -12, 85, -616, 55, 601, -622, 110, 424, -885, 641, -668, -289, 701, -584, -321, -385, 572, 1127, -738, -341, -646, -69, -577, 134, 83, 482, -407, 400, 617, -1256, -595, 496, -240, 358, -22, 61, 1147, 115, -564, 303, -772, -579, 171, 805, -89, -942, -493, 935, -66, 776, -1157, 373, 371, -1756, -378, -821, 518, -95, -728, -1023, 1442, 976, -545, -21, -695, -931, -327, 649, -95, 1819, -305, 2982, 86, 240, -664, -347, -337, 277, -323, 430, -899, 9, -211, 161, 822, -1389, -552, -451, -294, -873, -277, 1414, 89, 261, -699, -62, -407, 310, -344, -988, -445, 463, 778, 434, -942, -521, 428, 146, 697, -1205, -579, -125, 93, 748, -116, -310, 491, 1258, -611, 736, 82, 216, -1223, -474, -5, -1043, 320, -415, -734, -263, -606, 776, 1135, 1609, -1146, -897, -600, 275, -423, -748, -425, -432, -361, 289, 820, -10, 126, 1697, -476, 299, -518, -264, -404, -217, -422, 202, -75, -603, -252, 767, -278, 1203, -114, 277, -13, -624, -446, -229, 406, 648, -842, -161, 238, -570], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "4001.2.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "hecke_cutters": null, "qexp_display": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}